{
  "id": "2012.13216",
  "version": "v1",
  "published": "2020-12-24T12:24:01.000Z",
  "updated": "2020-12-24T12:24:01.000Z",
  "title": "Determinants and Plemelj-Smithies formulas",
  "authors": [
    "Duván Cardona",
    "Julio Delgado",
    "Michael Ruzhansky"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.DG",
    "math.OA",
    "math.SP"
  ],
  "abstract": "We establish Plemelj-Smithies formulas for classical Fredholm determinants by applying a recently introduced notion of invariant operators relative to a fixed decomposition of Hilbert spaces. The analysis also make use of the corresponding notion of full matrix-symbol. We also derive explicit formulas for determinants associated to elliptic operators on compact manifolds, compact Lie groups, and on homogeneous vector bundles over compact homogeneous manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-24T12:24:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact lie groups",
      "classical fredholm determinants",
      "homogeneous vector bundles",
      "full matrix-symbol",
      "compact manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}